Depending on where your tank is, you can cut a hole in the outside of your RV, mount a fill fitting and run a fill and vent line to your water tank. It all depends on where it is whether it is doable. You also need a couple of feet drop from the fill port to the top of the tank.
Powering directly from 12V DC is always better than through an inverter. But most TV "bricks" are now 19V like laptops. About ten years ago I searched long and hard for a TV with a 12V brick that I could cut off and wire directly and finally found one. But a recent check of TVs at Best Buy found none- all were either direct 110V plugins or 19V bricks.
Most RV electronic propane level readouts are only accurate to the nearest 1/4. Look at the propane level sender on the tank itself. It will be more accurate once you recognize that it never will be full, 80% at best.
I like the manual leveling Bigfoot levelers where you adjust each foot until it is level rather than pushing a button and doing it automatically.